Can One (Ever) Accurately Define Markets?

The ongoing debate about the role of market definition in antitrust cases addresses the usefulness and correct application of the Hypothetical Monopolist Test (HMT) as defined by the U.S. Department of Justice and the Federal Trade Commission in the Horizontal Merger Guidelines. These guidelines intend to identify the techniques that those agencies use to evaluate the potential anticompetitive effects of a merger. In this article, I examine the accuracy of the HMT. In applying the HMT, I consider two separate models. In each model, one knows the true extent of the product market. First, I apply the HMT in a linear differentiated demand model with n firms that each produce one symmetrically differentiated product, and derive conditions whereby m products would be considered to comprise a product market. I find that the test consistently underestimates the number of products in the relevant market in that setting, and the resulting relevant product markets are arbitrary subsets of the actual product market. The second model uses a quasi-linear utility specification, where the products enter the utility function additively. The only interaction between the two products occurs through the income effects of the budget constraint. Under certain conditions, the smallest possible product market as defined by the HMT must include at least one producer of the other product. Therefore, depending on the underlying parameters of the utility function, the HMT might either overestimate or underestimate the size of the relevant product market, sometimes producing purely arbitrary results.